A Superfluid Gyroscope with Cold Atomic Gases

A trapped Bose-Einstein condensed atomic gas containing a quantized vortex is predicted to exhibit precession after a sudden rotation of the confining potential. The equations describing the motion of the condensate are derived and the effects of superfluidity explicitly pointed out. The dependence of the precession frequency on the relevant parameters of the problem is discussed. The proposed gyroscope is well suited to explore rotational effects at the level of single quanta of circulation. PACS numbers: 03.75.Fi, 05.30.Jp, 32.80.Pj, 67.40.-w Typeset using REVTEX 1 After the realization of Bose-Einstein condensation [1] in magnetically trapped vapours of alkali atoms, cooled down to extremely low temperatures, the superfluid behaviour of these systems has become the object of extensive experimental work. This includes the study of rotational properties, like quantized vortices [2,3] and the quenching of the moment of inertia [4], as well as the reduction of dissipative effects [5]. The purpose of this work is to show that Bose-Einstein condensed (BEC) gases can be used to realize a quantum gyroscope where the effects of superfluidity show up in a very peculiar way. Superfluid gyroscopes have been already realized with liquid He [6] and He [7] and have been mainly used to investigate the nature of persistent currents in toroidal geometries. Most of experiments with helium gyroscopes operate with many quanta of circulation. Compared to liquid helium, trapped BEC gases are mesoscopic systems in the sense that the healing length, which provides a typical range of dynamic correlations and fixes the size of the vortex core, is smaller, but not extremely smaller than the size of the sample [8]. For the same reason the angular momentum Nh̄ carried by a single quantized vortex can have visible effects on the global motion of the condensate as we will prove in this letter. A further feature that characterizes these systems is the very peculiar type of confinement which yields new possibilities for exploring superfluid phenomena. Important gyroscopic effects associated with the occurrence of vortex lines have been already observed in trapped BEC gases [9–11]. The authors of [9] have succeeded in testing the quantization of the angular momentum of a single vortex line. To this purpose one generates a quadrupole deformation in the plane orthogonal to the vortex axis. The observed precession of the deformation is proportional to the angular momentum carried by the vortex, in accordance with the predictions of theory [12,13]. Notice that in this experiment the vortex line is not affected by the precession. The authors of [10] and [11] have instead observed the precession of a vortex line either displaced or tilted from the symmetry axis of the condensate. In this case the motion of the condensate is not affected at a macroscopic level and the precession involves the change of the density on a more microscopic scale, of the order of the size of the vortex core. 2 In the present work we discuss the macroscopic precession of the symmetry axis of a deformed condensate caused by the sudden rotation of the trap, in the presence of a quantized vortex line. This precession corresponds to a full rotation of the condensate in 3D, which preserves the intrinsic shape of the system. The geometry of the proposed gyroscope is illustrated in fig.1. The system consists of a dilute and cold gas of atoms with mass m confined by an axi-symmetric trap of harmonic shape: